Local layering

In a conventional 2d painting or compositing program, graphical objects are stacked in a user-specified global order, as if each were printed on an image-sized sheet of transparent film. In this paper we show how to relax this restriction so that users can make stacking decisions on a per-overlap basis, as if the layers were pictures cut from a magazine. This allows for complex and visually exciting overlapping patterns, without painstaking layer-splitting, depth-value painting, region coloring, or mask-drawing. Instead, users are presented with a layers dialog which acts locally. Behind the scenes, we divide the image into overlap regions and track the ordering of layers in each region. We formalize this structure as a graph of stacking lists, define the set of orderings where layers do not interpenetrate as consistent, and prove that our local stacking operators are both correct and sufficient to reach any consistent stacking. We also provide a method for updating the local stacking when objects change shape or position due to user editing - this scheme prevents layer updates from producing undesired intersections. Our method extends trivially to both animation compositing and local visibility adjustment in depth-peeled 3d scenes; the latter of which allows for the creation of impossible figures which can be viewed and manipulated in real-time.